{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Exactly solvable models for topological phases","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree"},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/78200"},{"label":"dc.language.iso","value":"en_US"},{"label":"dcterms.abstract","value":"Topological systems are characterized by some collection of features which remain unchanged under deformations of the Hamiltonian which leave the band gap open. The earliest examples of these were free fermion systems, allowing us to study the band structure to determine if a candidate material supports topological features. However, we can also ask the reversed question, i.e. Given a band gap, what topological features can be engineered?  This classification problem proved to have numerous answers depending on which extra assumptions we allow, producing many candidate phases. While free fermion topological features could be classified by their band structures (culminating in the 10-fold way), strongly interacting systems defied this approach, and so classification outstripped the construction of even the most elementary Hamiltonians, leaving us with a number of phases which could exist, but do not have a single strongly interacting representative. The purpose of this thesis is to resolve this in certain cases by constructing commuting projector models (CPM), a class of exactly solvable models, for two types of topological phases, known as symmetry enriched topological (SET) order and fermionic symmetry protected topological (SPT) phases respectively. After introducing the background and history of commuting projector models, we will move on to the details of how these Hamiltonians are built. In the first case, we construct a CPM for a SET, showing how to encode the necessary group cohomology data into a lattice model. In the second, we construct a CPM for a fermionic SPT, and find that we must include a combinatorial representation of a spin structure to make the model consistent. While these two projects were independent, they are linked thematically by a technique known as decoration, where extra data is encoded onto simple models to generate exotic phases."},{"label":"dcterms.available","value":"2018-03-22T22:39:17Z"},{"label":"dcterms.contributor","value":"Wei, Tzu-Chieh."},{"label":"dcterms.creator","value":"Tarantino, Nicolas Alessandro"},{"label":"dcterms.dateAccepted","value":"2018-03-22T22:39:17Z"},{"label":"dcterms.dateSubmitted","value":"2018-03-22T22:39:17Z"},{"label":"dcterms.description","value":"Department of Physics."},{"label":"dcterms.extent","value":"90 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/78200"},{"label":"dcterms.issued","value":"2017-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2018-03-22T22:39:17Z (GMT). No. of bitstreams: 1\nTarantino_grad.sunysb_0771E_13421.pdf: 2195551 bytes, checksum: 02d1c65f7b5d8702d7b21a42eb90f40d (MD5)\n  Previous issue date: 2017-08-01"},{"label":"dcterms.subject","value":"Exactly solvable models"},{"label":"dcterms.title","value":"Exactly solvable models for topological phases"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/26%2F71%2F00%2F26710027808982210177641816733702809930/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/26%2F71%2F00%2F26710027808982210177641816733702809930","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}